Calculate [tex]$\frac{7}{10} \times \frac{2}{3}$[/tex]. Give your answer in its simplest form.
Answer (2)
Multiply the numerators and denominators: 10 7 × 3 2 = 10 × 3 7 × 2 = 30 14 .
Find the greatest common divisor (GCD) of 14 and 30, which is 2.
Divide both the numerator and the denominator by the GCD: 30 ÷ 2 14 ÷ 2 = 15 7 .
The simplified fraction is 15 7 .
Explanation
Understanding the Problem We need to calculate the product of two fractions, 10 7 and 3 2 , and express the result in its simplest form.
Multiplying the Fractions First, we multiply the numerators and the denominators of the two fractions: 10 7 × 3 2 = 10 × 3 7 × 2 = 30 14 .
Finding the Greatest Common Divisor (GCD) Next, we simplify the fraction 30 14 by finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 14 and 30 is 2.
Simplifying the Fraction Now, we divide both the numerator and the denominator by their GCD: 30 14 = 30 ÷ 2 14 ÷ 2 = 15 7 . Therefore, the simplified form of the fraction is 15 7 .
Final Answer The product of 10 7 and 3 2 in its simplest form is 15 7 .
Examples
In baking, if a recipe calls for 10 7 of a cup of flour and you only want to make 3 2 of the recipe, you would multiply these fractions to determine how much flour you need. The calculation 10 7 × 3 2 = 15 7 tells you that you need 15 7 of a cup of flour. This ensures you maintain the correct proportions for your adjusted recipe, preventing it from being too dry or too wet. Understanding fraction multiplication is essential for scaling recipes accurately.
The product of 10 7 and 3 2 can be calculated by multiplying the numerators to get 14 and the denominators to get 30, resulting in the fraction 30 14 . This fraction can then be simplified by dividing both the numerator and denominator by their GCD, which is 2, leading to the final answer of 15 7 .
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